Question

Integration of (3x+4)^2

Answer 1

Answer:

Hope you like my explanation.

Answer 2

respect to x

∫

(

3

x

+

4

)

2

d

x

Let

u

=

3

x

+

4

. Then

d

u

=

3

d

x

, so

1

3

d

u

=

d

x

. Rewrite using

u

and

d

u

.

Let

u

=

3

x

+

4

. Find

d

u

d

x

.

3

1

Divide

3

by

1

.

3

Rewrite the problem using

u

and

d

u

.

∫

u

2

1

3

d

u

Combine

u

2

and

1

3

.

∫

u

2

3

d

u

Since

1

3

is constant with respect to

u

, move

1

3

out of the integral.

1

3

∫

u

2

d

u

By the Power Rule, the integral of

u

2

with respect to

u

is

1

3

u

3

.

1

3

(

1

3

u

3

+

C

)

Simplify.

Simplify.

1

3

(

1

3

u

3

)

+

C

Combine fractions.

Combine

1

3

and

u

3

.

1

3

⋅

u

3

3

+

C

Multiply

1

3

and

u

3

3

.

u

3

3

⋅

3

+

C

Multiply

3

by

3

.

u

3

9

+

C

Replace all occurrences of

u

with

3

x

+

4

.

(

3

x

+

4

)

3

9

+

C

Reorder terms.

1

9

(

3

x

+

4

)

3

+

C